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Lecture 1

PHYS 101 Lecture Notes - Lecture 1: Spherical Earth, Noon, Escape Velocity

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PHYS 101

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001.1 The Sky: Certain as the Sunrise
sun rise in the East, and set in the West
observe means actually experiencing something for yourself.
When everyone who repeats an observation experiences the same
thing, the observation is said to be reproducible
At a very young age, infants learn to go from simple observations
to mental models of what they are observing. The simplest sort of
model is called "object permanence" and just means that
something can be hidden or out of sight and still exist. In the case
of the Sun rising and setting, this model suggests that it is always
the same Sun, which means that the Sun must somehow get back
to the eastern horizon after setting in the west.
A worthwhile model of a situation must reproduce what is actually
observed --- It must save the appearances.
Pythagoras (born in 570 BCE) guessed that the Earth must be
shaped like a sphere because that is the most elegant and
harmonious shape that he could think of. It is not clear that
observation played much of a role in his thinking
flat earth model was rejected because it was ugly
the nice thing about a spherical Earth model is that it has no edge
and only one number is needed to specify the model completely,
the radius R of the sphere.
Aristotle (born in 384 BCE) pointed out If the Earth is a sphere,
then gravity pulls things toward its center. However, if gravity
pulls things toward the center of the Earth, that pretty much
explains why the surface does not fall. It has already fallen as far
as it can, which also explains the spherical shape, since all of its
parts are as close to the center as they can get.
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Aristotle pointed out that a spherical Earth would explain why
southern constellations are seen higher in the sky in places that are
farther to the south. spherical Earth would cast a curved shadow on
the Moon and that is exactly what is seen during an eclipse of the
Eratosthenes of Cyrene (born 276 BCE) knew that on the day of
the summer solstice, the noon Sun near the city of Syene was
straight overhead. At that same time in the city of Alexandria,
north of Syene, the Sun was 7 and 12/60 degrees south of
o Earth radius to Syene and an Earth radius to Alexandria was
7 and 12/60 degrees. That angle is just 1/50 of a full circle
(360 degrees), so the distance from Alexandria to Syene must
be 1/50 of the distance completely around
o distance from Alexandria to Syene was about 5000 stadia.
The circumference of the Earth had to be 50×5000 stadia or
250,000 stadia. A stadion is the length of a footrace stadium.
circumference = 250,000 × 157.5 meters = 39,375 kilometers
o The currently accepted value for the Earth's circumference
over the poles: 40,008 kilometers.
spherical model of the Earth and a little geometry, Eratosthenes'
measurement of the circumference gives us the radius:
The stars look as if they are attached to a sphere that surrounds the
earth, the Celestial Sphere. We now know that stars are really at
different distances from the Earth, but we still use the Celestial
Sphere model as a convenient map of the stars.
The Celestial Sphere appears to rotate from East to West, carrying
each star completely around in slightly less than 24 hours. The
time for one rotation is called a sidereal day (4 minutes less than
24 hrs)
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A fixed pattern of stars is called a constellation.
These patterns are partly illusions because stars that look close
together in the sky may be at very different distances from us.
pointer stars in the Big Dipper are used to locate Polaris, a star
very close to the North Celestial Pole.
three stars of Orions "belt" are used to locate the star Sirius, one of
the very brightest stars in the sky.
The brightest star has a name that begins with the greek-letter
alpha. The next brightest begins with the greek letter beta, and then
gamma and then delta.
Some constellations, such as Orion, behave very much like the Sun,
rising in the East and setting in the West. Other constellations circle the
Celestial Poles, never rising or setting. (circumpolar constellations).
Here, in the middle latitudes of the Northern Hemisphere, the easiest
circumpolar constellations to recognize are
Ursa Minor (contains Polaris and the Little Dipper)
Ursa Major (contains the Big Dipper)
Proper motion- stars are actually moving
Apparent motion- the stars seem to be rotating but its actually the
solar day is defined to be the time from one solar noon to the next
and is the time needed for the earth to rotate by about 361°. That
amount of time is defined to be 24 hours. A sidereal day is the
time needed for the earth to rotate by 360° and is four minutes
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